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Multivariate Ratio Analysis (MRA): R-scripts and tutorials for calculating Shape PCA, Ratio Spectra and LDA Ratio Extractor

Baur, Hannes; Leuenberger, Christoph

This package contains some scripts written in the R language (R Core Team 2020) that allow the calculation of various morphometric methods published by Baur & Leuenberger (2011). Later these methods were addressed under the name "Multivariate Ratio Analysis (MRA)" (see Baur et al. 2014). The scripts were originally provided by the authors in an electronic supplementary file together with the original paper, and later in slightly modified form also by Baur et al. (2014). However, it is our wish to publish them in a manner that they may be cited separately and also be updated when necessary.

The package contains the main scripts in two files:


Important note: In the script of the LDA Ratio Extractor the case for more than 2 groups is now also included. This case was described by Baur & Leuenberger (2011, p. 817), but was left out from the R-script originally published in Systematic Biology. We think that the implementation is a welcome addition to the entire set of methods provided by MRA.

For both scripts, separate tutorials are available:
Tutorial_1_ Shape_PCA.R

It is recommended to work through these brief tutorials, starting with the first one.

A dataset (from Baur et al. 2014) is supplied as well:

In order to avoid any troubles, make sure that all files are put into one and the same folder. R-Studio is recommended for performing the R-scripts (especially for beginners).

PDFs of the two papers cited below are also provided in the package.


Citation: You may use the citation of the package as indicated by Zenodo on this webpage. Do also cite the original paper by Baur & Leuenberger (2011, citation below), as only this article contains the mathematical background and scientific context concerning the methods.

If you have questions please contact:
Hannes Baur, Natural History Museum Bern, Bernastrasse 15, 3005 Bern, Switzerland, Email:


Cited references

Baur H, Kranz-Baltensperger Y, Cruaud A, Rasplus J-Y, Timokhov AV, Gokhman VE (2014) Morphometric analysis and taxonomic revision of Anisopteromalus Ruschka (Hymenoptera: Chalcidoidea: Pteromalidae) - an integrative approach. Systematic Entomology 39: 691–709.

Baur H, Leuenberger C (2011) Analysis of ratios in multivariate morphometry. Systematic Biology 60: 813–825.

R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL


Further reading (recommended examples of the use of MRA in taxonomy and functional morphology)

Huber C, Schnitter PH (2020) Nebria (Pseudonebriola) tsambagarav sp. nov., a new alpine species from the Mongolian Altai (Coleoptera, Carabidae). Alpine Entomology 4: 29–38.

Petrović TG, Vukov TD, Tomašević Kolarov N (2017) Morphometric ratio analyses: Locomotor mode in anurans. Comptes Rendus Biologies 340: 250–257.


What is new in v1.02

- addition of main reference (Baur & Leuenberger 2011) in tutorials and function files
- minor change in presentation of information concerning LDA_Ratio_Extractor_vY.YY.R
- correction of spelling errors
Files (4.3 MB)
Name Size
57.2 kB Download
Baur and Leuenberger - 2011 - Analysis of ratios in multivariate morphometry.pdf
293.2 kB Download
Baur et al. - 2014 - Morphometric analysis and taxonomic revision of An.pdf
3.9 MB Download
6.7 kB Download
10.6 kB Download
Tutorial_1_ Shape_PCA.R
17.3 kB Download
5.3 kB Download
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